The subset of space occupied by the grains of a flowing powder at any point in time can be thought of as a realization of a random set [1]}, [2]}. These sets are random because their structure is unpredictable between
different replicates or realizations. Their internal structure is disordered,
but the disordered pattern of grains is neither stationary nor ergodic.
There is no simple or obvious way to coordinatize the internal structure of an ensemble of
disordered patterns, and so these patterns must be summarized
by sets of descriptive statistics. These statistics may be based on
single patterns observed at a fixed time in each realization or replicate,
or they could be constructed from many patterns observed at fixed
times along the joint trajectory of the grains.
